add: 220104-CN
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03734becc9
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@ -2,114 +2,103 @@
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#include <cstring>
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#include <cstdio>
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// #define LOCAL
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#define LOCAL
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class Solution {
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private:
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inline static int d[50][50];
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inline static bool vis[50][50];
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static int dp(int cat, int mouse, const std::vector<std::vector<int>>& graph, bool isCatMove
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#ifdef LOCAL
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, int depth = 0
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#endif
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) {
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if (d[cat][mouse] != -1) {
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#ifdef LOCAL
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for (int i = 0; i < depth; i++, std::printf(" "));
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std::printf("(%d, %d) is calculated before, returning %d.\n", cat, mouse, d[cat][mouse]);
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std::fflush(stdout);
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#endif
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return d[cat][mouse];
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}
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if (vis[cat][mouse]) {
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#ifdef LOCAL
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for (int i = 0; i < depth; i++, std::printf(" "));
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std::printf("(%d, %d) is trapped in a loop state, returning 0.\n", cat, mouse);
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std::fflush(stdout);
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#endif
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return 0;
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}
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if (mouse == 0) {
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#ifdef LOCAL
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for (int i = 0; i < depth; i++, std::printf(" "));
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std::printf("(%d, %d) is won by the mouse, returning 1.\n", cat, mouse);
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std::fflush(stdout);
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#endif
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return 1;
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}
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if (cat == mouse) {
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#ifdef LOCAL
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for (int i = 0; i < depth; i++, std::printf(" "));
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std::printf("(%d, %d) is won by the cat, returning 2.\n", cat, mouse);
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std::fflush(stdout);
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#endif
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return 2;
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}
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vis[cat][mouse] = true;
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int ans, r, hasNext = 0;
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int results[3]{};
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if (isCatMove) { // Next is mouse to move
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for (const int& catNext : graph[cat]) {
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if (catNext == 0) continue;
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#ifdef LOCAL
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for (int i = 0; i < depth; i++, std::printf(" "));
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std::printf("(%d, %d) [Cat] -> Iterating into (%d, %d)\n", cat, mouse, catNext, mouse);
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std::fflush(stdout);
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#endif
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r = dp(catNext, mouse, graph, false
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#ifdef LOCAL
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, 1 + depth
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#endif
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);
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++results[r];
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}
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if (results[2]) {
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ans = 2;
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} else if (results[0]) {
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ans = 0;
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} else {
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ans = 1;
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}
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} else { // Next is cat
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for (const int& mouseNext : graph[mouse]) {
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if (mouseNext == cat) continue;
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#ifdef LOCAL
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for (int i = 0; i < depth; i++, std::printf(" "));
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std::printf("(%d, %d) [Mouse] -> Iterating into (%d, %d)\n", cat, mouse, cat, mouseNext);
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std::fflush(stdout);
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#endif
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r = dp(cat, mouseNext, graph, true
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#ifdef LOCAL
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, 1 + depth
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#endif
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);
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++results[r];
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hasNext += (r != 0);
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}
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if (!hasNext) {
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ans = 2;
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} else if (results[1]) {
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ans = 1;
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} else if (results[0]) {
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ans = 0;
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} else {
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ans = 2;
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}
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}
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vis[cat][mouse] = false;
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#ifdef LOCAL
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for (int i = 0; i < depth; i++, std::printf(" "));
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std::printf("(%d, %d) [Next move %s] is returning %d.\n", cat, mouse, isCatMove ? "cat" : "mouse", ans);
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std::fflush(stdout);
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#endif
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return d[cat][mouse] = ans;
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}
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// dp[][][0]: previous moved is mouse, [1] cat.
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inline static int d[50][50][2];
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inline static bool vis[50][50][2];
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public:
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static int catMouseGame(const std::vector<std::vector<int>>& graph) {
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std::memset(d, -1, sizeof d);
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std::memset(vis, 0, sizeof vis);
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return dp(2, 1, graph, false);
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const auto n = graph.size();
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for (int i = 1; i < 50; ++i) {
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// initial states
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d[i][i][0] = d[i][i][1] = 2;
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d[i][0][0] = d[i][0][1] = d[0][i][0] = d[0][i][1] = 1;
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}
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while (true) {
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int cnt = 0;
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// i <- position of cat
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for (int i = 0; i < n; ++i) {
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// j <- position of mouse
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for (int j = 0; j < n; ++j) {
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if (d[i][j][0] == -1) {
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/**
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* Cat to move:
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* Cat is very clever, if cat is possible to not be fail,
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* he will not. And, if it can immediately make the mouse
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* fail, it will.
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*/
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int& currentState = d[i][j][0];
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bool stateChanged = false;
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int failState = 0, totalState = 0;
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for (int k : graph[i]) {
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if (!k) continue;
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const int& previousState = d[k][j][1];
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++totalState;
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switch (previousState) {
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case 2: // Cat wins
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// std::printf("(%d, %d, %d) <- Cat can immediately wins at (%d, %d, %d)\n", i, j, 0, k, j, 1);
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currentState = 2;
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stateChanged = true;
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break;
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case 1: // Mouse wins
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++failState;
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default: ; // ignored when uncertain
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}
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}
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// The cat can no longer wins
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// std::printf("(%d, %d, %d) Cat <- failState %d / totalState %d\n", i, j, 0, failState, totalState);
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if (failState == totalState)
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stateChanged = (currentState = 1);
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cnt += stateChanged;
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}
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if (d[i][j][1] == -1) {
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/**
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* Mouse to move:
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* Mouse is very clever, if the mouse is possible to
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* not be fail, it will not. And, if it can win
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* immediately, it will!
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*/
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int& currentState = d[i][j][1];
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bool stateChanged = false;
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int failState = 0, totalState = 0;
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for (int k : graph[j]) {
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const int& previousState = d[i][k][0];
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++totalState;
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switch (previousState) {
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case 1: // Mouse wins
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// std::printf("(%d, %d, %d) <- Mouse can immediately wins at (%d, %d, %d)\n", i, j, 1, i, k, 0);
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currentState = 1;
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stateChanged = true;
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break;
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case 2: // Cat wins
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++failState;
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default: ; // ignored when uncertain
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}
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}
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// The mouse can no longer wins
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// std::printf("(%d, %d, %d) Mouse <- failState %d / totalState %d\n", i, j, 1, failState, totalState);
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if (failState == totalState)
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stateChanged = (currentState = 2);
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cnt += stateChanged;
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}
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}
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}
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if (!cnt) break;
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}
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switch (d[2][1][1]) {
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case 2:
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return 2;
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case 1:
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return 1;
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default:
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return 0;
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}
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}
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};
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@ -119,12 +108,20 @@ int main() {
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// {{2, 3}, {3, 4}, {0, 4}, {0, 1}, {1, 2}} -> 1
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// {{3,4},{3,5},{3,6},{0,1,2},{0,5,6},{1,4},{2,4}} -> 0
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// {{4},{2,3,5},{1,5,3},{1,2},{0},{1,2}} -> 2
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// {{5,6},{3,4},{6},{1,4,5},{1,3,5},{0,3,4,6},{0,2,5}} -> 2
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std::printf("%d\n", Solution::catMouseGame({{1, 3}, {0}, {3}, {0, 2}}));
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std::printf("%d\n", Solution::catMouseGame({{2, 5}, {3}, {0, 4, 5}, {1, 4, 5}, {2, 3}, {0, 2, 3}}));
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std::printf("%d\n", Solution::catMouseGame({{2, 5},
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{3},
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{0, 4, 5},
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{1, 4, 5},
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{2, 3},
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{0, 2, 3}}));
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std::printf("%d\n", Solution::catMouseGame({{2, 3}, {3, 4}, {0, 4}, {0, 1}, {1, 2}}));
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std::printf("%d\n", Solution::catMouseGame({{3,4},{3,5},{3,6},{0,1,2},{0,5,6},{1,4},{2,4}}));
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std::printf("%d\n", Solution::catMouseGame({{4},{2,3,5},{1,5,3},{1,2},{0},{1,2}}));
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std::printf("%d\n", Solution::catMouseGame({{5,6},{3,4},{6},{1,4,5},{1,3,5},{0,3,4,6},{0,2,5}}));
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return 0;
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}
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